Math Problem Statement
Solution
The image contains two mathematical problems where and represent the last two digits of a student identification number (NIM). In the example given, for a NIM ending in "61", and .
The two questions are:
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Find the solution set of .
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Find the solution set of .
Now, let's break down and solve these questions using the example values of and .
Question 1:
Solve .
With and , the equation becomes: We can break this inequality into two cases based on the absolute value:
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Case 1: , so
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Case 2: , so
Therefore, the solution to the inequality is or , but only holds when .
Thus, the final solution set is:
Question 2:
Solve .
Substitute and into the inequality: Simplify:
Now, we need to solve the inequality: This also splits into two cases:
- Case 1:
Do you want to explore further solutions or have clarifications?
Here are 5 follow-up questions for practice:
- How does the absolute value affect the range of solutions?
- Can you derive a general solution for inequalities involving absolute values?
- What are the properties of rational inequalities?
- How does adding constants inside absolute values impact the solution set?
- What strategies help simplify complex fractions in inequalities?
Tip: Always check the domain of your variable in inequalities before concluding the solution set.
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Math Problem Analysis
Mathematical Concepts
Algebra
Inequalities
Absolute Value
Rational Expressions
Formulas
3x - 5 < |x + 3a + 2b|
|2a + b + (2a + 3b)/(2x + a + b)| > a + 2b
Theorems
Absolute Value Theorem
Properties of Inequalities
Suitable Grade Level
Grade 10-12